As described in “Optical Differential Quadrature Phase-Shift Key (oDQPSK) for High Capacity Optical Transmission” by R. A. Griffin et al., Optical Fiber Communication Conference and Exhibit, USA. March 2003, WX6, pp. 367-368, the DQPSK scheme is a modulation scheme excellent in wavelength usage efficiency, wavelength dispersion tolerance and polarized wave dispersion tolerance, and application to various optical communication systems requiring these advantages is proposed (for example, JP2004-516743A). The configuration and operation of a general DQPSK optical communication system will be described below with reference to FIGS. 1 to 3, with an optical transmission apparatus and optical receiving apparatus using the DQPSK modulation scheme, which are disclosed in Patent Document 1, as an example.
FIG. 1 is a block diagram showing a configuration example of a modulation section of a general optical transmission apparatus and a demodulation section of a general optical receiving apparatus. FIG. 2A is a signal constellation diagram showing the phase state of general DQPSK optical transmission signal Es(t). FIG. 2B is a time chart showing an example of phase variation of general DQPSK optical transmission signal Es(t). FIG. 3 is a time chart showing DQPSK optical transmission signal Es(t) and demodulated signal Rx.
In FIG. 1, optical transmission apparatus 900 is provided with DQPSK encoding section 901, optical carrier generation section 902 and DQPSK modulation section 903. In optical carrier generation section 902, a laser diode is usually used as a CW (continuous wave) light source.
Optical receiving apparatus 920 is provided with optical splitter 923, delay interferometers 921 and 922, and balancing-type photoelectric converters 924 and 925. Delay interferometer 921 is provided with arm 921a having an optical transmission path for making delay time τ and arm 921b for fixedly giving a π/4 phase shift and, when necessary, for fixedly giving fine-adjustment phase Φ0. Delay interferometer 922 is provided with arm 922a having an optical transmission path for making delay time τ and arm 922b for fixedly giving a −π/4 phase shift and, when necessary, for fixedly giving fine-adjustment phase Φ0.
In optical transmission apparatus 900, optical carrier generation section 902 generates an optical carrier with frequency v0 and outputs it to DQPSK modulation section 903. DQPSK modulation section 903 phase-modulates the optical carrier with frequency v0 any of four values located at an interval of π/4 as shown in FIG. 2A, in accordance with signals ET1 and ET2 to generate DQPSK signal Es(t). DQPSK encoding section 901 performs encoding of transmitted data d1 and d2 corresponding to DQPSK modulation and outputs encoded signals ET1 and ET2 to DQPSK modulation section 903.
As shown in FIGS. 2A and 2B, phase θ of an optical signal is any of [π/4, 3π/4, 5π/4, 7π/4] for each symbol. The original signal has been encoded by DQPSK encoding section 901 and mapped to Δθ which is the phase difference between a signal and the immediately previous signal. Δθ is any of the four values of [0, π/2, π, 3π/2]. Since transmission signal Es(t) is a signal obtained by modulating optical carrier frequency v0 with phase information θ(t), it can be expressed by the following expression (1).
[Expression 1]Es(t)=exp{i[2πv0t+θ(t)]}  (1)
Here, θ(t) takes any of the values of [π/4, 3π/4, 5π/4, 7π/4]. Since each symbol has four values, that is, 2-bit information, the symbol rate is B/2 [symbols/s] and the symbol interval is τ=2/B [seconds] for transmission capacity B [bits/s].
When optical signal Es(t) expressed by the above expression (1) arrives, it is separated into two optical signals by optical splitter 923 of optical receiving apparatus 920. One is sent to delay interferometer 921, and the other to delay interferometer 922. The operation of delay interferometer 921 will be described below as an example.
Delay interferometer 921 further branches the inputted optical signal into two, delays one by τ at arm 921a, and phase-shifts the other by π/4 at arm 921b. By delaying one optical signal by τ, it is possible to cause the other optical signal to interfere with an optical signal before one symbol interval the signals and extract phase difference Δθ(t)=θ(t)−θ(t−τ). Two optical signals E1(t) and E2(t) before the interference can be expressed by the following expressions (2).
                    [                  Expression          ⁢                                          ⁢          2                ]                                                                                  E            ⁢                                                  ⁢            1            ⁢                          (              t              )                                =                                    ⅇ                              ⅈ                ⁢                                  π                  2                                                      ⁢            exp            ⁢                          {                              ⅈ                ⁡                                  [                                                            2                      ⁢                      π                      ⁢                                                                                          ⁢                                                                        v                          0                                                ⁡                                                  (                                                      t                            -                            π                                                    )                                                                                      +                                          θ                      ⁡                                              (                                                  t                          -                          τ                                                )                                                                              ]                                            }                                      ⁢                                  ⁢                              E            ⁢                                                  ⁢            2            ⁢                          (              t              )                                =                      exp            ⁢                                                  ⁢                          {                              ⅈ                ⁡                                  [                                                            2                      ⁢                      π                      ⁢                                                                                          ⁢                                                                        v                          0                                                ⁡                                                  (                          t                          )                                                                                      +                                          ϕ                      0                                        +                                          θ                      ⁡                                              (                        t                        )                                                              +                                          π                      4                                                        ]                                            }                                                          (        2        )            
Here, Φ0 is a fine-adjustment phase term for, when causing an optical carrier with frequency v0 to interfere τ hours before with a carrier, aligning the phases of both carriers. Adjustment can be performed with the use of a phase modulator for π/4 shift.
When two optical signals E1(t) and E2(t) are caused to interfere with each other, strengths I1(t) and I2(t) of the optical signals outputted from delay interferometer 921 can be expressed by the following expressions (3).
                    [                  Expression          ⁢                                          ⁢          3                ]                                                                                  I            ⁢                                                  ⁢            1                    =                                                                                                          E                    ⁢                                                                                  ⁢                    1                    ⁢                                          (                      t                      )                                                        +                                                            ⅇ                                              ⅈ                        ⁢                                                  π                          2                                                                                      ⁢                    E                    ⁢                                                                                  ⁢                    2                    ⁢                                          (                      t                      )                                                                                                  2                        ∝                          1              +                              cos                ⁡                                  (                                                            2                      ⁢                      πτ                      ⁢                                                                                          ⁢                                              v                        0                                            ⁢                      τ                                        +                                          ϕ                      0                                        +                    Δθ                    +                                          π                      4                                                        )                                                                    ⁢                                  ⁢                              I            ⁢                                                  ⁢            2                    =                                                                                                                                ⅇ                                              ⅈ                        ⁢                                                  π                          2                                                                                      ⁢                    E                    ⁢                                                                                  ⁢                    1                    ⁢                                          (                      t                      )                                                        +                                      E                    ⁢                                                                                  ⁢                    2                    ⁢                                          (                      t                      )                                                                                                  2                        ∝                          1              -                              cos                ⁡                                  (                                                            2                      ⁢                      π                      ⁢                                                                                          ⁢                      τ                      ⁢                                                                                          ⁢                                              v                        0                                            ⁢                      τ                                        +                                          ϕ                      0                                        +                    Δθ                    +                                          π                      4                                                        )                                                                                        (        3        )            
Therefore, the difference signal therebetween is expressed by the following expression (4).
                    [                  Expression          ⁢                                          ⁢          4                ]                                                                                  I            ⁢                                                  ⁢            1                    -                      I            ⁢                                                  ⁢            2                          ∝                  2          ⁢                      cos            ⁡                          (                                                2                  ⁢                  π                  ⁢                                                                          ⁢                                      v                    0                                    ⁢                  τ                                +                                  ϕ                  0                                +                                  Δ                  ⁢                                                                          ⁢                  θ                                +                                  π                  4                                            )                                                          (        4        )            
When Φ0 is adjusted to align the phase with that of a carrier before one symbol interval the signals, the following expression (5) is satisfied.
[Expression 5]2πv0τ+Φ0=2πN (N is an integer.)  (5)
Therefore, the following expression (6) is obtained from expressions (4) and (5).
                    [                  Expression          ⁢                                          ⁢          6                ]                                                                                  I            ⁢                                                  ⁢            1            ⁢                          (              t              )                                -                      I            ⁢                                                  ⁢            2            ⁢                          (              t              )                                      ∝                  cos          ⁡                      (                                          Δ                ⁢                                                                  ⁢                                  θ                  ⁡                                      (                    t                    )                                                              +                              π                4                                      )                                              (        6        )            
Therefore, electrical signal x(t) expressed by the following expression (7) is obtained by square-law detecting two optical signals I1 and I2 by balancing-type photoelectric converter 924.
                    [                  Expression          ⁢                                          ⁢          7                ]                                                                                  x            ⁡                          (              t              )                                ∝                                    I              ⁢                                                          ⁢              1              ⁢                              (                t                )                                      -                          I              ⁢                                                          ⁢              2              ⁢                              (                t                )                                              ∝                                    cos              ⁢                                                          ⁢                              Δθ                ⁡                                  (                  t                  )                                                      -                          sin              ⁢                                                          ⁢                              θ                ⁡                                  (                  t                  )                                                                    =                  {                                                    1                                            for                                                                                                        Δ                      ⁢                                                                                          ⁢                                              θ                        ⁡                                                  (                          t                          )                                                                                      =                    0                                    ,                                                            3                      ⁢                                                                                          ⁢                      π                                        2                                                                                                                        -                  1                                                            for                                                                                                        Δ                      ⁢                                                                                          ⁢                                              θ                        ⁡                                                  (                          t                          )                                                                                      =                                                                                                                                            ⁢                        π                                            2                                                        ,                  π                                                                                        (        7        )            
Similarly, since delay interferometer 922 causes interference with what is obtained by phase-shifting a signal of shorter arm 922b by −π/4, the difference signal therebetween, I3(t)−I4(t), is expressed by the following expression (8).
                    [                  Expression          ⁢                                          ⁢          8                ]                                                                                  I            ⁢                                                  ⁢            3            ⁢                          (              t              )                                -                      I            ⁢                                                  ⁢            4            ⁢                          (              t              )                                      ∝                  cos          ⁡                      (                                          2                ⁢                π                ⁢                                                                  ⁢                                  v                  0                                ⁢                τ                            +                              ϕ                0                            +                              Δ                ⁢                                                                  ⁢                                  θ                  ⁡                                      (                    t                    )                                                              -                              π                4                                      )                                              (        8        )            
Since expression (5) is satisfied, electrical signal y(t) expressed by the following expression (9) is obtained by square-law detecting two optical signals I3 and I4 by balancing-type photoelectric converter 925.
                    [                  Expression          ⁢                                          ⁢          9                ]                                                                                  y            ⁡                          (              t              )                                ∝                                    I              ⁢                                                          ⁢              3              ⁢                              (                t                )                                      -                          I              ⁢                                                          ⁢              4              ⁢                              (                t                )                                              ∝                                    cos              ⁢                                                          ⁢                              Δθ                ⁡                                  (                  t                  )                                                      +                          sin              ⁢                                                          ⁢                              θ                ⁡                                  (                  t                  )                                                                    =                  {                                                    1                                            for                                                                                                        Δ                      ⁢                                                                                          ⁢                                              θ                        ⁡                                                  (                          t                          )                                                                                      =                    0                                    ,                                      π                    2                                                                                                                        -                  1                                                            for                                                                                                        Δ                      ⁢                                                                                          ⁢                                              θ                        ⁡                                                  (                          t                          )                                                                                      =                                                                  3                        ⁢                                                                                                  ⁢                        π                                            2                                                        ,                  π                                                                                        (        9        )            
An example of output from balancing-type photoelectric converters 924 and 925 described above is shown in FIG. 3. At DQPSK encoding section 901 on the transmission side, it is encoded so that electrical signals x(t) and y(t) obtained on the receiving side correspond to the original signals (signals d1 and d2 before encoding on the transmission side).